E-state Indices

The EState program calculates atom-type and bond-type E-state indices. Five groups of indices are calculated. Each group of indices is represented by a single index in E-state indices group. In fact all of them are index groups with variable number of indices. Each index has a name that depends on atom or bond type and value. Examples E-state indices are shown in Table 1 and description of the calculation procedure is given by Hall and Kier.

1. E-state atom type indices.
     Basic set of indices consists of electrotopological state indices proposed by Hall and Kier [1-3].

2. E-state extended atom type indices.
     A set of extended indices for O and N atoms was also developed to take into account their functional groups and neighborhood[4-5]. The name of an extended index consisted of the name of original E-state index and name extension that depended on the atom neighborhood. All nitrogen atoms were divided into five groups. These groups include aliphatic (extension "(al)") and aromatic amines ("(ar)"), salts of amines ("(salt)"), nitrogens of nitro and nitroso groups ("(nitro)") and other types of nitrogen ("oth"). In the same way  oxygen atoms of OH groups (sOH E-state index) were classified as atoms of alcohols ("(alc)"), phenols ("(phen)"), carboxylic acids ("(acid)"), amino acids ("(zwit)"). Among the atoms of double-bonded oxygen (dO E-state index) the atoms of ketones ("(keto)"), carboxylic acids ("(acid)"), esters ("(ester)"), amides (("amid)"), nitro and nitroso groups ("(nitro)"), sulfones and sulfoxides ("(sulfo)") were distinguished.

3. E-state bond indices.
     The bond-type E-state indices are used to describe two atom states. Firstly, an intrinsic state value is assigned to each edge and then the perturbation from each other edge was computed and added to the analyzed edge value (MolconnZ manual, chapter 2). The bond E-state value was then computed as

Iij = (Ii + Ij)/2 , BES_ij = I_ij + ??I_ij/(  + 1)²                    (1)

where   is computed as the average r_ij for the atoms in the two bonds. These values were computed for individual bonds and then were collected for each type of the bond in the molecule.
     Names of the bond type electrotopological state indices are different from those proposed by Hall and Kier [1-3], although they are basically the same. These names also start with bond order indicator (e1, e2, e3 and ea for single, double, triple and aromatic bonds respectively) and are followed by two atom type names. Atom type names include atom name and the number of skeletal bonds for that atom. Finally an indication of the unused bonds  of each atom is given. The unused bonds are always mentioned in our implementation. This makes it different from original version by Kier and Hall where an indication of unused bonds is given "if necessary". For example, MolconnZ gives e1C2C3d for bond 3 in our example (see Table 1.3) while our program gives e1C2C3dd. A special type of nitrogen N== is introduced for the nitrogen with two double and one single bonds (ddsN type). This was done to avoid charged groups and to distinguish this type from the other nitrogen atoms bonded to three other skeletal atoms.

Table 1. E-state Indices Calculated for a hypothetical structure.

SMILES Code: C(=O)(O)C=CCc1c(N)cc(N(=O)=O)cc1Cl; Formula: C10H9N2O4Cl; Molecular weight, MW= 256.65; Number of non-hydrogen atoms, NA=17; Number of hydrogen atoms, NH=9.

Table 1.1 Atom-type E-state indices (sums over all the atoms of the considered type)

 Table 1.2 Extended atom-type E-state indices (sums over all atoms of the specified type with certain chemical functionality)

Table 1.3 Molecular Bond E-state indices (sums of the values for all the bonds of the above bond types)

REFERENCES
(1) Kier, L. B.; Hall, L. H. An Electrotopological State Index for Atoms in Molecules. Pharm. Res. 1990, 7, 801-807.
(2) Hall, L. H.; Kier, L. B. Electrotopological State Indices for Atom Types: A Novel Combination of Electronic, Topological, and Valence State Information. J. Chem. Inf. Comput. Sci. 1995, 35, 1039-1045.
(3) Kier, L. B.; Hall, L. H. Molecular Structure Description: TheElectrotopological State; Academic Press: London, 1999.
(4) Huuskonen, J. J.; Villa, A. E. P.; Tetko, I. V. Prediction of Partition Coefficient Based on Atom-Type Electrotopological State Indices. J. Pharm. Sci. 1999, 88, 229-233.
(5) Huuskonen, J. J.; Livingstone, D. J.; Tetko, I. V. Neural Network Modeling for Estimation of Partition Coefficient Based on Atom-type Electrotopological State Indices. J. Chem. Inf. Comput. Sci. 2000, 40, 947-955.

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